Question: $J$ $K$ $L$ If: $ JL = 85$, $ JK = 5x + 9$, and $ KL = 3x + 4$, Find $KL$.
Answer: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {5x + 9} + {3x + 4} = {85}$ Combine like terms: $ 8x + 13 = {85}$ Subtract $13$ from both sides: $ 8x = 72$ Divide both sides by $8$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $KL$ $ KL = 3({9}) + 4$ Simplify: $ {KL = 27 + 4}$ Simplify to find ${KL}$ : $ {KL = 31}$